What did the smoking oven and the fiery torch denote?
Rashi: Gehinom - a hint that the nations concerned would fall into Gehinom.
Targum Yonasan: It hints at Gehinom, into which the Resha'im will fall. 1
Ramban: The oven containing the fiery torch, fire symbolizes the Shechinah, 2 which passed between the pieces to enact the B'ris Bein ha'Besarim (the covenant between Hashem and Avraham as mentioned in the next Pasuk, and to which we refer every day in Pesukei de'Zimrah).
Hadar Zekenim (Devarim 32:27): The oven hints to subjugation under the kingdoms, and the fire, to Gehinom. Avraham's seed is destined to suffer one of them; Hashem asked him to choose one. He chose subjugation (see the following Pasuk). 3
According to the Midrash, the "furnace of smoke" represents subjugation to foreign kingdoms, while the "torch of fire" represents Gehinom, both of which would threaten Am Yisrael. When Yisrael involve themselves with Torah and with Avodah of the Beis ha'Mikdash, they will be saved from them. (Opinions differ as to whether Avraham chose that his descendants be subjected to the foreign kingdoms, or whether Avraham chose Gehinom, only for Hashem to veto that choice.) Why does the furnace represent the kingdoms, and the torch represent Gehinom? How do Torah and the Beis ha'Mikdash protect us? Where are these two alluded to in the Pasuk?
Maharal (Gevuros Hashem Ch. 8, p. 51) 1 : Smoke does not destroy intensively, and so the foreign kingdoms are compared to smoke, in contrast to Gehinom represented by fire itself. Through this covenant between the parts of the animals, Hashem hints to the merit of the Korbanos, which includes both the Avodah itself and the Torah laws associated with them. The kingdoms and Gehinom represent futility (Tohu) 2 and destruction (He'eder) respectively. We will be saved from these through Torah, which is the essence of reality in terms of the Sechel, and through the Beis ha'Mikdash, which is the "heart" of existence, and perfection in this world. The difference of opinion In the Midrash revolves around whether Avraham chose foreign subjugation, which would eventually come to an end, or Gehinom because Tzadikim are naturally repulsed by evildoers. Hashem chose foreign subjugation for us, because He is merciful, and brings suffering upon a person only in order to atone for his shortcomings.
According to Rashi (on Pasuk 10) the oven of smoke and the torch of fire were the Sheluchim (the agents) of the Shechinah
Why does it say "Asher Avar" (past tense)? The fiery torch passed between the pieces now!
Peninim mi'Shulchan ha'Gra: Avraham merited the Bris Bein ha'Besarim because he had passed through the fire of the furnace (when he refused to bow to Nimrod's idol). This is a hint. It is not the simple meaning of the verse.
QUESTIONS ON RASHI
Rashi writes: "'And it was (va'Yehi), the sun had set' - This [usage of the word va'Yehi] is like [in the verse], "and it was, they were emptying their sacks (42:35)." What is Rashi coming to explain?
Gur Aryeh: In 42:35, the verse opens with the singular, "va'Yehi, " and follows with the plural, "they"! Rather, that verse means, "and this is what happened next, that as they were emptying...." Our verse is similarly difficult, for "va'Yehi" is masculine, while "ha'Shemesh Ba'ah" is feminine. Rather, it means, "And this is what happened next, the sun had set."